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CN108510499A - A kind of carrying out image threshold segmentation method and device based on fuzzy set and Otsu - Google Patents

A kind of carrying out image threshold segmentation method and device based on fuzzy set and Otsu Download PDF

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CN108510499A
CN108510499A CN201810128721.9A CN201810128721A CN108510499A CN 108510499 A CN108510499 A CN 108510499A CN 201810128721 A CN201810128721 A CN 201810128721A CN 108510499 A CN108510499 A CN 108510499A
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otsu
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孙林
王亚文
范梦雨
赵明
李梦莹
孟新超
王蓝莹
殷腾宇
赵婧
张云萍
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Henan Normal University
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Abstract

The present invention relates to image segmentation fields, and in particular to a kind of carrying out image threshold segmentation method and device based on fuzzy set and Otsu.The present invention is primarily based on fuzzy set and gives new enhanced fuzzy membership function;Then the discretization method for utilizing mean square deviation, constructs the inter-class variance of Otsu;Renyi entropy theories are finally combined, the Renyi entropys that weight calculation provides image are introduced, the threshold value for reusing maximum Renyi entropys completes image segmentation.The present invention compares traditional Threshold Segmentation Algorithm, has preferable advantage, while also with good stability and segmentation effect in the accuracy in segmenting edge and the robustness to noise, can effectively improve the precision of image segmentation.

Description

一种基于模糊集和Otsu的图像阈值分割方法及装置A Method and Device for Image Threshold Segmentation Based on Fuzzy Sets and Otsu

技术领域technical field

本发明涉及图像分割领域,具体涉及一种基于模糊集和Otsu的图像阈值分割方法及装置。The invention relates to the field of image segmentation, in particular to an image threshold segmentation method and device based on fuzzy sets and Otsu.

背景技术Background technique

图像分割一般是指根据图像中的灰度、颜色、纹理、形状和边缘等特征把图像划分成若干个互不重叠的目标和背景两个区域,并使这些特征在同一区域内呈现出相似性,而不同区域呈现出明显的差异性。Image segmentation generally refers to dividing the image into several non-overlapping target and background regions according to the features such as grayscale, color, texture, shape and edge in the image, and making these features show similarity in the same region. , and there are obvious differences in different regions.

在众多的图像分割方法中,阈值分割法因其简单有效、计算复杂度低以及性能稳定等特点,成为图像分割中应用最广泛的分割技术。其关键是如何选取阈值,以便获得最优分割效果。阈值分割方法大致可以分为两类:全局阈值分割法和局部阈值分割法。全局阈值分割法根据整个图像直方图信息选择一个单阈值将图像划分成两部分;局部阈值分割法是将原始图像划分成多个较小的图像,并对每个子图像选取相应的阈值。Among many image segmentation methods, the threshold segmentation method has become the most widely used segmentation technology in image segmentation because of its simplicity, effectiveness, low computational complexity, and stable performance. The key is how to choose the threshold in order to obtain the optimal segmentation effect. Threshold segmentation methods can be roughly divided into two categories: global threshold segmentation methods and local threshold segmentation methods. The global threshold segmentation method selects a single threshold based on the entire image histogram information to divide the image into two parts; the local threshold segmentation method divides the original image into multiple smaller images, and selects the corresponding threshold for each sub-image.

现有技术已经提出大量的阈值选取方法,结合智能算法寻求不同准则下的最佳阈值,在不同应用领域取得了较好的应用效果。Sezgin和Sankur在2004年撰写了《Surveyover image thresholding techniques and quantitative performance evaluation》(Journal of Electronic Imaging,2004,13(1):146-166.),对40多种全局阈值分割法做了综合比较,指出基于Otsu、最大熵的阈值分割法是应用较为广泛的两种全局阈值分割法。Otsu算法是基于整幅图像的统计特性,实现图像阈值的自动选取,分割效果良好,在实际中得到了广泛应用。就Otsu而言,优点是算法简单,且当目标与背景的面积相差不大时,能够很有效地对图像进行分割。但是,这种算法的计算量较大,很难适应实时处理;同时,当图像中目标与背景的面积相差很大时,分割效果不佳,表现为直方图没有明显的双峰或者两峰的大小相差很大,当目标与背景的灰度有较大重叠时也无法准确地将两者分开。导致出现这种现象的原因是一方面该方法忽略了图像的空间信息,另一方面将图像灰度分布作为分割图像的依据,于是对噪声也相当敏感。因而,在实际应用中,总是将Otsu与其他方法结合使用。A large number of threshold selection methods have been proposed in the prior art, combined with intelligent algorithms to find the optimal threshold under different criteria, and achieved good application results in different application fields. Sezgin and Sankur wrote "Surveyover image thresholding techniques and quantitative performance evaluation" (Journal of Electronic Imaging, 2004, 13(1): 146-166.) in 2004, and made a comprehensive comparison of more than 40 global threshold segmentation methods. It is pointed out that threshold segmentation methods based on Otsu and maximum entropy are two widely used global threshold segmentation methods. The Otsu algorithm is based on the statistical characteristics of the whole image, and realizes the automatic selection of the image threshold. The segmentation effect is good, and it has been widely used in practice. As far as Otsu is concerned, the advantage is that the algorithm is simple, and when the area of the target and the background is not much different, the image can be segmented very effectively. However, this algorithm has a large amount of calculation and is difficult to adapt to real-time processing; at the same time, when the area of the target and the background in the image is very different, the segmentation effect is not good, showing that the histogram has no obvious double peaks or two peaks The size is very different, and when the grayscale of the target and the background has a large overlap, the two cannot be separated accurately. The reason for this phenomenon is that on the one hand, the method ignores the spatial information of the image, and on the other hand, the gray distribution of the image is used as the basis for segmenting the image, so it is also quite sensitive to noise. Thus, in practice, Otsu is always used in combination with other methods.

发明内容Contents of the invention

本发明的目的是提供一种基于模糊集和Otsu的图像阈值分割方法及装置,用以解决现有方法进行图像分割时效果不佳的问题。The object of the present invention is to provide a method and device for image threshold segmentation based on fuzzy sets and Otsu to solve the problem of poor effect of image segmentation in existing methods.

为实现上述目的,本发明提供了一种基于模糊集和Otsu的图像阈值分割方法,包括:To achieve the above object, the invention provides a method for image threshold segmentation based on fuzzy sets and Otsu, including:

方法方案一,包括以下步骤:Method scheme one includes the following steps:

使用模糊算法对原图像进行模糊增强处理;Use the fuzzy algorithm to perform fuzzy enhancement processing on the original image;

对增强处理后的新图像进行归一化处理;Normalize the enhanced new image;

分别求出Renyi熵的阈值th1和Otsu的阈值th2;Calculate the threshold th1 of Renyi entropy and the threshold th2 of Otsu respectively;

分别求出所述阈值th1对应的类间方差和所述阈值th2对应的类间方差;Respectively find the inter-class variance corresponding to the threshold th1 and the inter-class variance corresponding to the threshold th2;

根据所述阈值th1和所述阈值th2对应的所述类间方差计算得到所述类间方差的权重S1以及所述Renyi熵对应的权重S2Calculate the weight S 1 of the inter-class variance and the weight S 2 corresponding to the Renyi entropy according to the inter-class variance corresponding to the threshold th1 and the threshold th2 ;

求得分割阈值th=S1th2+S2th1;根据所述分割阈值th进行图像分割。Obtain the segmentation threshold th=S 1 th2+S 2 th1; perform image segmentation according to the segmentation threshold th.

方法方案二,在方法方案一的基础上,求出Renyi熵的阈值th1和Otsu的阈值th2的公式包括:Method 2: On the basis of method 1, the formulas for calculating Renyi’s entropy threshold th1 and Otsu’s threshold th2 include:

其中,th1为Renyi熵的阈值;th2为Otsu的阈值;EO为原图像目标域的Renyi熵;EB为原图像背景域的Renyi熵;L为原图像的灰度级;t为灰度阈值,且t取值为[0,L–1];w0为第一类灰度出现的比例,w1为第二类灰度出现的比例,所述第一类灰度和第二类灰度根据所述灰度阈值t划分;σ0为第一类灰度对应图像的灰度均方差,σ1为第二类灰度对应图像的灰度均方差;σ为所述原图像经过所述模糊增强和所述归一化处理后的灰度平均值。Among them, th1 is the threshold of Renyi entropy; th2 is the threshold of Otsu; E O is the Renyi entropy of the target domain of the original image; E B is the Renyi entropy of the background domain of the original image; L is the gray level of the original image; t is the gray level Threshold, and the value of t is [0, L–1]; w 0 is the proportion of the first gray scale, w 1 is the proportion of the second gray scale, the first gray scale and the second gray scale The grayscale is divided according to the grayscale threshold t; σ0 is the grayscale mean square error of the image corresponding to the first type of grayscale, and σ1 is the grayscale mean square error of the image corresponding to the second type of grayscale; The average gray value after the blur enhancement and the normalization processing.

方法方案三,在方法方案一或者方法方案二的基础上,求出所述类间方差的过程包括:Method scheme three, on the basis of method scheme one or method scheme two, the process of calculating the variance between classes includes:

Renyi熵的阈值th1的类间方差σ2和σ3为:The between-class variances σ2 and σ3 of the threshold th1 of Renyi entropy are:

Otsu的阈值th2的类间方差σ0和σ1为:The between-class variances σ0 and σ1 of Otsu's threshold th2 are:

其中,pi为像素点数为ni的灰度级出现的概率;uT为所述原图像的灰度平均值,L1=0,L2=L–1。Among them, p i is the probability of occurrence of the gray level with the number of pixels n i ; u T is the average gray level of the original image, L1=0, L2=L–1.

方法方案四,在方法方案三的基础上,计算得到所述类间方差的权重的过程包括:Method scheme four, on the basis of method scheme three, the process of calculating the weight of the inter-class variance includes:

其中,S1为所述类间方差的权重,且S2=1–S1Wherein, S 1 is the weight of the inter-class variance, and S 2 =1−S 1 .

方法方案五,在方法方案四的基础上,所述归一化处理包括:Method scheme five, on the basis of method scheme four, the normalization process includes:

采用min或者max算子进行边缘提取;Use min or max operator for edge extraction;

将提取的边缘数据进行截断处理;Truncating the extracted edge data;

所述截断处理为:The truncation process is:

其中,Tr(uij)为所述边缘数据;uij为所述模糊算法中的隶属函数。Wherein, Tr(u ij ) is the edge data; u ij is the membership function in the fuzzy algorithm.

本发明还提供了一种基于模糊集和Otsu的图像阈值分割装置,包括:The present invention also provides an image threshold segmentation device based on fuzzy sets and Otsu, comprising:

装置方案一,包括处理器和存储器,所述处理器存储有实现如下方法的指令:The device solution one includes a processor and a memory, and the processor stores instructions for implementing the following method:

使用模糊算法对原图像进行模糊增强处理;Use the fuzzy algorithm to perform fuzzy enhancement processing on the original image;

对增强处理后的新图像进行归一化处理;Normalize the enhanced new image;

分别求出Renyi熵的阈值th1和Otsu的阈值th2;Calculate the threshold th1 of Renyi entropy and the threshold th2 of Otsu respectively;

分别求出所述阈值th1对应的类间方差和所述阈值th2对应的类间方差;Respectively find the inter-class variance corresponding to the threshold th1 and the inter-class variance corresponding to the threshold th2;

根据所述阈值th1和所述阈值th2对应的所述类间方差计算得到所述类间方差的权重S1以及所述Renyi熵对应的权重S2Calculate the weight S 1 of the inter-class variance and the weight S 2 corresponding to the Renyi entropy according to the inter-class variance corresponding to the threshold th1 and the threshold th2 ;

求得分割阈值th=S1th2+S2th1;根据所述分割阈值th进行图像分割。Obtain the segmentation threshold th=S 1 th2+S 2 th1; perform image segmentation according to the segmentation threshold th.

装置方案二,在装置方案一的基础上,求出Renyi熵的阈值th1和Otsu的阈值th2的公式包括:Device scheme 2, on the basis of device scheme 1, the formulas for calculating the threshold th1 of Renyi entropy and the threshold th2 of Otsu include:

其中,th1为Renyi熵的阈值;th2为Otsu的阈值;EO为原图像目标域的Renyi熵;EB为原图像背景域的Renyi熵;L为原图像的灰度级;t为灰度阈值,且t取值为[0,L–1];w0为第一类灰度出现的比例,w1为第二类灰度出现的比例,所述第一类灰度和第二类灰度根据所述灰度阈值t划分;σ0为第一类灰度对应图像的灰度均方差,σ1为第二类灰度对应图像的灰度均方差;σ为所述原图像经过所述模糊增强和所述归一化处理后的灰度平均值。Among them, th1 is the threshold of Renyi entropy; th2 is the threshold of Otsu; E O is the Renyi entropy of the target domain of the original image; E B is the Renyi entropy of the background domain of the original image; L is the gray level of the original image; t is the gray level Threshold, and the value of t is [0, L–1]; w 0 is the proportion of the first gray scale, w 1 is the proportion of the second gray scale, the first gray scale and the second gray scale The grayscale is divided according to the grayscale threshold t; σ0 is the grayscale mean square error of the image corresponding to the first type of grayscale, and σ1 is the grayscale mean square error of the image corresponding to the second type of grayscale; The average gray value after the blur enhancement and the normalization processing.

装置方案三,在装置方案一或者装置方案二的基础上,求出所述类间方差的过程包括:Device scheme three, on the basis of device scheme one or device scheme two, the process of calculating the variance between the classes includes:

Renyi熵的阈值th1的类间方差σ2和σ3为:The between-class variances σ2 and σ3 of the threshold th1 of Renyi entropy are:

Otsu的阈值th2的类间方差σ0和σ1为:The between-class variances σ0 and σ1 of Otsu's threshold th2 are:

其中,pi为像素点数为ni的灰度级出现的概率;uT为所述原图像的灰度平均值,L1=0,L2=L–1。Among them, p i is the probability of occurrence of the gray level with the number of pixels n i ; u T is the average gray level of the original image, L1=0, L2=L–1.

装置方案四,在装置方案三的基础上,计算得到所述类间方差的权重的过程包括:Device scheme four, on the basis of device scheme three, the process of calculating the weight of the variance between classes includes:

其中,S1为所述类间方差的权重,且S2=1–S1Wherein, S 1 is the weight of the inter-class variance, and S 2 =1−S 1 .

装置方案五,在装置方案四的基础上,所述归一化处理包括:Device scheme five, on the basis of device scheme four, the normalization process includes:

采用min或者max算子进行边缘提取;Use min or max operator for edge extraction;

将提取的边缘数据进行截断处理;Truncating the extracted edge data;

所述截断处理为:The truncation process is:

其中,Tr(uij)为所述边缘数据;uij为所述模糊算法中的隶属函数。Wherein, Tr(u ij ) is the edge data; u ij is the membership function in the fuzzy algorithm.

本发明的有益效果是:首先基于模糊集给出了新的模糊增强隶属函数;然后利用均方差的离散化方法,构造了Otsu的类间方差;最后结合Renyi熵理论,引入权重计算给出图像的Renyi熵,再使用最大Renyi熵的阈值完成图像分割。本发明相比传统的阈值分割算法,在分割边缘的准确性和对噪声的鲁棒性上具有较好的优势,同时也具有良好的稳定性和分割效果,可以有效地提高图像分割的精度。The beneficial effects of the present invention are: firstly, a new fuzzy enhanced membership function is given based on the fuzzy set; then, the discretization method of the mean square error is used to construct the inter-class variance of Otsu; finally, combined with the Renyi entropy theory, the weight calculation is introduced to give the image Renyi entropy, and then use the threshold of the maximum Renyi entropy to complete image segmentation. Compared with the traditional threshold segmentation algorithm, the present invention has better advantages in the accuracy of edge segmentation and robustness to noise, and also has good stability and segmentation effect, and can effectively improve the accuracy of image segmentation.

附图说明Description of drawings

图1是本发明方法的流程图;Fig. 1 is a flow chart of the inventive method;

图2是对Lena图像采用Pal-King方法迭代一次的效果图;Fig. 2 is an effect diagram of one iteration of the Lena image using the Pal-King method;

图3是对Lena图像采用Pal-King方法迭代二次的效果图;Fig. 3 is the rendering of the second iteration of the Lena image using the Pal-King method;

图4是对Lena图像采用本发明的方法迭代一次的效果图;Fig. 4 is the effect figure that adopts the method of the present invention to iterate once to Lena image;

图5是Cameraman图像;Figure 5 is a Cameraman image;

图6是Cameraman模糊增强图像;Figure 6 is a Cameraman blur enhanced image;

图7是采用传统Otsu算法对Cameraman图像的分割结果;Figure 7 is the segmentation result of the Cameraman image using the traditional Otsu algorithm;

图8是采用本发明的方法对Cameraman图像的分割结果;Fig. 8 adopts the method of the present invention to the segmentation result of Cameraman image;

图9是Cameraman图像的直方图;Figure 9 is a histogram of the Cameraman image;

图10是Goldhill图像;Figure 10 is a Goldhill image;

图11是Goldhill模糊增强图像;Figure 11 is a Goldhill fuzzy enhanced image;

图12是采用传统Otsu算法对Goldhill图像的分割结果;Fig. 12 is the segmentation result of the Goldhill image using the traditional Otsu algorithm;

图13是采用本发明的方法对Goldhill图像的分割结果;Fig. 13 adopts the method of the present invention to the segmentation result of Goldhill image;

图14是Goldhill图像的直方图。Figure 14 is a histogram of the Goldhill image.

具体实施方式Detailed ways

下面结合附图对本发明做进一步详细的说明。The present invention will be described in further detail below in conjunction with the accompanying drawings.

为了解决传统的Otsu算法对含有噪声、光照不均图像分割效果不明显、不准确等问题,提出了一种基于模糊集和Otsu的图像阈值分割方法及装置。首先,基于模糊集给出了新的模糊增强隶属函数;然后,利用均方差的离散化方法构造了Otsu的类间方差;最后,结合Renyi熵理论,引入权重计算给出图像的Renyi熵,再使用最大Renyi熵的阈值完成图像分割。In order to solve the problem that the traditional Otsu algorithm has inconspicuous and inaccurate segmentation effects on images containing noise and uneven illumination, an image threshold segmentation method and device based on fuzzy sets and Otsu is proposed. Firstly, a new fuzzy enhanced membership function is given based on fuzzy sets; then, Otsu’s inter-class variance is constructed using the discretization method of mean square error; finally, combined with Renyi entropy theory, weight calculation is introduced to give the Renyi entropy of the image, and then Image segmentation is done using a threshold of the maximum Renyi entropy.

根据模糊集的概念,一幅大小为M×N的图像,灰度级为L,可以表示为如下的一个M×N的模糊矩阵:According to the concept of fuzzy sets, an image with a size of M×N and a gray level of L can be expressed as an M×N fuzzy matrix as follows:

其中矩阵中的各个元素表示图像中像素(i,j)的灰度xij相对于原图像中对应灰度级x的隶属度,这是一个求模糊分布的问题。在经典的模糊增强算法中,Pal和King提出了一种模糊增强算法,其中所使用的隶属函数为:Each element in the matrix Indicates the membership degree of the gray level x ij of the pixel (i, j) in the image relative to the corresponding gray level x in the original image. This is a problem of finding a fuzzy distribution. Among the classic fuzzy enhancement algorithms, Pal and King proposed a fuzzy enhancement algorithm in which the membership function used is:

其中参数Fd、Fe与uij的形状有关,可以通过渡越点确定。一般情况下,取Fe=2得到uij后,要对图像进行模糊增强处理,采用如下变换:Among them, the parameters F d and F e are related to the shape of u ij and can be determined by the transition point. In general, after taking F e = 2 to obtain u ij , the image needs to be blurred and enhanced, and the following transformation is adopted:

uij=Tr(uij)=T1(Tr-1(uij)) (3)u ij =T r (u ij )=T 1 (T r-1 (u ij )) (3)

其中r=1,2,…。where r = 1, 2, . . .

当uij>0.5时,增大uij的值;当uij≤0.5时,减小uij的值。对uij进行逆变换,经过模糊增强后,得到图像X′,X′中的像素(i,j)的灰度值:When u ij >0.5, increase the value of u ij ; when u ij ≤0.5, decrease the value of u ij . Perform inverse transformation on u ij , after blur enhancement, get the gray value of the pixel (i, j) in the image X', X':

xij=T-1(uij) (5)x ij =T -1 (u ij ) (5)

其中,T-1(·)为公式(2)中T(·)的逆运算。Among them, T -1 (·) is the inverse operation of T(·) in formula (2).

Ostu方法以图像的灰度直方图为依据,以目标和背景的类间方差最大为阈值选取准则。其基本思想:设原始灰度图像共有L个灰度级,某一灰度级的像素点数为ni,图像的总像素为N,则可以得到各灰度级出现的概率:The Ostu method is based on the gray histogram of the image, and the maximum variance between the classes of the target and the background is used as the threshold selection criterion. The basic idea: assuming that the original grayscale image has L grayscale levels in total, the number of pixels of a certain grayscale level is n i , and the total pixels of the image are N, then the probability of occurrence of each grayscale level can be obtained:

在图像分割中,按照图像灰度级用阈值t将灰度划分为两类,即C0类(灰度级为0,1,2,…,t)和C1类(灰度级为t+1,t+2,…,L–1),t的范围由归一化处理确定,t的初始值为灰度级存在的情况下(灰度级出现的概率不等于0)对应的最小值。C0和C1出现的比例分别为:In image segmentation, according to the gray level of the image, the gray level is divided into two categories with the threshold t, namely C 0 class (gray level is 0, 1, 2,..., t) and C 1 class (gray level is t +1,t+2,...,L–1), the range of t is determined by normalization processing, and the initial value of t is the minimum value corresponding to the presence of gray levels (the probability of gray level occurrence is not equal to 0). value. The proportions of C 0 and C 1 appearing are:

因此,C0均值和C1均值分别为:Therefore, the C 0 mean and C 1 mean are respectively:

整幅图像的灰度平均值为:The average gray value of the entire image is:

所以,类间方差为:So, the between-class variance is:

σB 2=ω0(u0-uT)21(u1-uT)2 (12)σ B 2 =ω 0 (u 0 -u T ) 21 (u 1 -u T ) 2 (12)

让t在[0,L–1]之间取值,使图像的两部分距离最大的阈值就是Otsu法的最佳阈值,其表达式:Let t take a value between [0, L–1], and the threshold that maximizes the distance between the two parts of the image is the optimal threshold of the Otsu method, and its expression:

一、改进的模糊增强1. Improved blur enhancement

设一幅图像为X,其大小为M×N,灰度级为L,最大灰度为L–1,xij表示图像的第(i,j)个像素的灰度值,则新的隶属函数可定义为:Suppose an image is X, its size is M×N, the gray level is L, the maximum gray level is L–1, x ij represents the gray value of the (i, j)th pixel of the image, then the new membership A function can be defined as:

运用重复递归调用对图像进行如下增强处理:The image is enhanced using repeated recursive calls as follows:

uij=Tr(uij)=Tr(Tr-1(uij)) (15)u ij =T r (u ij )=T r (T r-1 (u ij )) (15)

其中r=1,2,…,∞。where r=1,2,...,∞.

经过多次回归调用,算子Tr(uij)增强了较大隶属度值,抑制了较小隶属度值。After multiple regression calls, the operator T r (u ij ) enhances the larger membership degree value and suppresses the smaller membership degree value.

归一化处理。采用“min”或“max”算子进行边缘提取,将提取的“边缘”数据Tr(uij)进行截断处理:Normalized processing. Use the "min" or "max" operator for edge extraction, and truncate the extracted "edge" data T r (u ij ):

经过式(17)的截断处理,可将图像数据从模糊域转换到图像的空间域,即图像的灰度域。After the truncation processing of formula (17), the image data can be converted from the fuzzy domain to the spatial domain of the image, that is, the grayscale domain of the image.

为了验证改进的模糊增强对图像分割的有效性,选取Lena图像,分别采用传统模糊增强中Pal-King方法和本发明改进的模糊增强方法对其进行增强处理。仿真实验结果如图2-图4所示。图4中本发明的方法迭代1次的图像增强效果优于图3中Pal-King方法迭代2次。改进后的模糊增强处理保留了图像中低灰度值的边缘信息,进而保留了图像信息的完整性,有助于下一步的图像分割。In order to verify the effectiveness of the improved fuzzy enhancement on image segmentation, the Lena image is selected and enhanced by the Pal-King method in the traditional fuzzy enhancement and the improved fuzzy enhancement method of the present invention. The simulation experiment results are shown in Fig. 2-Fig. 4. The image enhancement effect of the method of the present invention in FIG. 4 after one iteration is better than that of the Pal-King method in FIG. 3 after two iterations. The improved fuzzy enhancement process preserves the edge information of low gray value in the image, and then preserves the integrity of image information, which is helpful for the next step of image segmentation.

二、Renyi熵2. Renyi entropy

熵是信息论中描述不确定因素的基本方法,而图像的边界分布是最具有不确定性的。因而,图像中目标和背景交界处的熵最大(信息量最大),熵反映了图像的总体轮廓。下面给出Renyi熵的基本概念:设目标O和目标B的概率分别为:Entropy is the basic method to describe uncertain factors in information theory, and the boundary distribution of images is the most uncertain. Therefore, the entropy (the largest amount of information) at the junction of the target and the background in the image is the largest, and the entropy reflects the overall outline of the image. The basic concept of Renyi entropy is given below: Let the probabilities of target O and target B be respectively:

且有PO(t)+PB(t)=1。由此对应于图像目标域和背景域的Renyi熵可分别定义为:And there is P O (t)+P B (t)=1. Therefore, the Renyi entropy corresponding to the image target domain and background domain can be defined as:

则图像总体的Renyi熵定义为:Then the overall Renyi entropy of the image is defined as:

其中α>0,α为一个参数,本文设置为0.7。Where α>0, α is a parameter, which is set to 0.7 in this paper.

根据最大熵图像分割的阈值选取原则,某个阈值t能够使得式(22)取得最大值,则其为最佳分割阈值,即:According to the threshold selection principle of maximum entropy image segmentation, a certain threshold t can make formula (22) obtain the maximum value, then it is the optimal segmentation threshold, namely:

三、改进的Otsu模型3. Improved Otsu model

通常情况下,不同的对象其内部的灰度比较均匀,分布在对象间的交界及其附近的像素灰度变化一般较大,而均方差值能够体现灰度的离散程度,即灰度分布的均匀性。因此,边界的灰度变化可用图像的均方差值来近似反映。Normally, different objects have relatively uniform internal gray levels, and the gray levels of pixels distributed at the junction between objects and their vicinity generally vary greatly, and the mean square error value can reflect the degree of dispersion of gray levels, that is, the gray level distribution uniformity. Therefore, the gray level change of the boundary can be approximately reflected by the mean square error value of the image.

给定图像C0、C1的灰度均方差σ0、σ1分别表示为:The gray mean square error σ 0 and σ 1 of the given images C 0 and C 1 are expressed as:

整幅图像经过处理后的灰度平均值表示为:The average gray value of the entire image after processing is expressed as:

类间方差表示为:The between-class variance is expressed as:

σB1 2=w00-σ)2+w11-σ)2 (27)σ B1 2 =w 00 -σ) 2 +w 11 -σ) 2 (27)

将Renyi熵方法计算的阈值t带入公式(24)和(25),计算其方差分别为σ2 2和σ3 2,可以将图像分割为两个目标:Bring the threshold t calculated by the Renyi entropy method into formulas (24) and (25), and calculate its variance as σ 2 2 and σ 3 2 , respectively, and the image can be divided into two targets:

其中,L1=0,L2=L–1。Among them, L1=0, L2=L-1.

最大类间方差方法计算的阈值对应的权重表示为:The weight corresponding to the threshold calculated by the maximum between-class variance method is expressed as:

则Renyi熵计算的阈值对应的权重为1–S。Then the weight corresponding to the threshold calculated by Renyi entropy is 1–S.

本发明方法结合Renyi熵和改进的Otsu模型,提出了基于模糊集和Otsu的图像阈值分割算法(FSO-ITS),如图1所示,其具体步骤描述如下:The inventive method combines Renyi entropy and improved Otsu model, has proposed the image threshold segmentation algorithm (FSO-ITS) based on fuzzy set and Otsu, as shown in Figure 1, its specific steps are described as follows:

步骤1:输入原图像;Step 1: Input the original image;

步骤2:运用新的隶属函数,对原图像进行模糊增强处理;Step 2: use the new membership function to perform fuzzy enhancement processing on the original image;

步骤3:对增强后的图像进行归一化处理;Step 3: normalize the enhanced image;

步骤4:分别求出Renyi熵和改进的Otsu的阈值th1和th2;Step 4: Calculate Renyi entropy and improved Otsu thresholds th1 and th2 respectively;

步骤5:分别求出th1的类间方差σ2和σ3以及th2的类间方差σ0和σ1Step 5: Calculate the inter-class variance σ 2 and σ 3 of th1 and the inter-class variance σ 0 and σ 1 of th2 respectively;

步骤6:将th2的类间方差与总的类间方差之比作为权重S;Step 6: Use the ratio of the inter-class variance of th2 to the total inter-class variance as the weight S;

步骤7:利用权重计算图像Renyi熵、类间方差之和达到最大时的阈值th,最后分割图像。Step 7: Use weights to calculate the threshold th when the sum of image Renyi entropy and inter-class variance reaches the maximum, and finally segment the image.

上述步骤中,包括公式:In the above steps, the formula is included:

四、实验结果与分析4. Experimental results and analysis

实验平台:Pentium4CPU3.0GHz的双核PC机,内存为2GB,操作系统为Windows7,运行环境为Matlab7.0。Experimental platform: Pentium4CPU3.0GHz dual-core PC with 2GB memory, Windows7 operating system and Matlab7.0 operating environment.

选用传统Otsu算法(Otsu N.A threshold selection method from gray-levelhistograms[J].IEEE Transactions on Systems,Man,and Cybernetics,1979,9(1):62-66.)、Renyi熵算法(Jizba P,Arimitsu T.Observability of Renyi's entropy[J].Physical Review E,2004,69(2):026128.)和本发明的FSO-ITS算法进行实验比较与分析。The traditional Otsu algorithm (Otsu N.A threshold selection method from gray-level histograms [J]. IEEE Transactions on Systems, Man, and Cybernetics, 1979, 9(1): 62-66.), Renyi entropy algorithm (Jizba P, Arimitsu T .Observability of Renyi's entropy[J].Physical Review E,2004,69(2):026128.) and the FSO-ITS algorithm of the present invention are compared and analyzed experimentally.

为了分析和验证提出的改进算法的实际效果,实验选取了一张256×256像素的标准图片Cameraman,如图5所示。首先对原始图像图5进行模糊增强处理,结果如图6所示。然后,分别采用传统Otsu算法和FSO-ITS算法对处理后的图像进行分割,其分割结果分别如图7和图8所示。图9为原始图像的直方图。In order to analyze and verify the actual effect of the proposed improved algorithm, a standard picture Cameraman with 256×256 pixels was selected in the experiment, as shown in Figure 5. Firstly, blur enhancement processing is performed on the original image Figure 5, and the result is shown in Figure 6. Then, the traditional Otsu algorithm and the FSO-ITS algorithm are used to segment the processed image, and the segmentation results are shown in Figure 7 and Figure 8, respectively. Figure 9 is a histogram of the original image.

由图7和图8直观可以看出,FSO-ITS算法分割获得的图像与传统Otsu算法相比,去噪效果较好,边缘较为清晰。为了进一步验证FSO-ITS算法的有效性,选取另一幅像素为512的标准图像Goldhill继续进行实验,如图10所示。图11为模糊增强后的结果,分割效果分别如图12和图13所示,图14为原始图像的直方图。It can be seen intuitively from Figure 7 and Figure 8 that compared with the traditional Otsu algorithm, the image obtained by FSO-ITS algorithm segmentation has better denoising effect and clearer edges. In order to further verify the effectiveness of the FSO-ITS algorithm, another standard image Goldhill with 512 pixels is selected to continue the experiment, as shown in Figure 10. Figure 11 is the result after blur enhancement, the segmentation effects are shown in Figure 12 and Figure 13 respectively, and Figure 14 is the histogram of the original image.

分析可知,FSO-ITS算法分割出的图像较为理想地把原始图像的目标区域和背景区域分开,能够充分反映出图像的边缘轮廓。The analysis shows that the image segmented by the FSO-ITS algorithm ideally separates the target area and the background area of the original image, and can fully reflect the edge contour of the image.

接下来利用图像分割阈值、峰值信噪比(PSNR)和信息熵等评判标准来客观地分析所提方法的优越性。其中,峰值信噪比是基于图像像素灰度值进行统计和平均计算,它是常用的衡量信号失真的指标。一般讲,PSNR越大,图像质量越好。下面给出PSNR的公式表示如下:Next, the superiority of the proposed method is objectively analyzed by using image segmentation threshold, peak signal-to-noise ratio (PSNR) and information entropy and other evaluation criteria. Among them, the peak signal-to-noise ratio is based on the statistical and average calculation of the image pixel gray value, which is a commonly used indicator to measure signal distortion. Generally speaking, the larger the PSNR, the better the image quality. The formula for PSNR given below is expressed as follows:

其中,MSE是编码前和解码后图像之间的均方误差。下面由表一给出3种算法的峰值信噪比实验结果比较。where MSE is the mean squared error between the pre-encoded and decoded images. Table 1 below gives the comparison of the experimental results of the peak signal-to-noise ratio of the three algorithms.

表一3种算法的峰值信噪比实验结果比较Table 1 Comparison of PSNR experimental results of the three algorithms

由表一所知,本发明提出的FSO-ITS算法的PSNR最大,说明该算法的失真最小,最为有效地保存了图像的原始信息。下面对实验结果进行信息熵的分析。图像信息熵是一种特征的统计形式。它反映了图像中包含信息量的多少,分割后的图像信息熵值越大,说明图像从源图像得到的信息量越大,分割图像细节越丰富,分割后的总效果越好。信息熵H(x)的公式表示如下:As known from Table 1, the PSNR of the FSO-ITS algorithm proposed by the present invention is the largest, indicating that the distortion of the algorithm is the smallest, and the original information of the image is preserved most effectively. The following is an analysis of the information entropy of the experimental results. Image information entropy is a statistical form of features. It reflects the amount of information contained in the image. The larger the information entropy value of the segmented image, the greater the amount of information obtained from the source image, the richer the details of the segmented image, and the better the overall effect of the segmented image. The formula of information entropy H(x) is expressed as follows:

表二3种算法的的信息熵实验结果比较Table 2 Comparison of information entropy experimental results of the three algorithms

从表二可以看出,本发明提出的FSO-ITS算法的信息熵最大,这就说明此算法从源图像得到的信息量最多,分割后的图像边缘更加完整,有效提高了图像分割的精度。As can be seen from Table 2, the information entropy of the FSO-ITS algorithm proposed by the present invention is the largest, which means that the algorithm obtains the largest amount of information from the source image, and the edge of the segmented image is more complete, effectively improving the accuracy of image segmentation.

由表一和表二的实验结果可知,与传统Otsu算法相比,FSO-ITS分割效果较优,边缘连续完整,细节处理较好;与传统Otsu算法和Renyi熵算法REA相比,FSO-ITS的峰值信噪比和信息熵最大,图像失真最小,分割精度最高。From the experimental results in Table 1 and Table 2, it can be seen that compared with the traditional Otsu algorithm, FSO-ITS has a better segmentation effect, continuous and complete edges, and better detail processing; compared with the traditional Otsu algorithm and Renyi entropy algorithm REA, FSO-ITS The peak signal-to-noise ratio and information entropy are the largest, the image distortion is the smallest, and the segmentation accuracy is the highest.

以上给出了本发明涉及的具体实施方式,但本发明不局限于所描述的实施方式,例如使用其他形式的模糊隶属函数,或者具体参数的设置,这样形成的技术方案是对上述实施例进行微调形成的,这种技术方案仍落入本发明的保护范围内。The specific implementations involved in the present invention have been provided above, but the present invention is not limited to the described implementations, such as using other forms of fuzzy membership functions, or the setting of specific parameters, the technical solution formed in this way is to carry out the above-mentioned embodiment Formed by fine-tuning, this technical solution still falls within the protection scope of the present invention.

Claims (10)

1.一种基于模糊集和Otsu的图像阈值分割方法,其特征在于,包括以下步骤:1. an image threshold segmentation method based on fuzzy sets and Otsu, is characterized in that, comprises the following steps: 使用模糊算法对原图像进行模糊增强处理;Use the fuzzy algorithm to perform fuzzy enhancement processing on the original image; 对增强处理后的新图像进行归一化处理;Normalize the enhanced new image; 分别求出Renyi熵的阈值th1和Otsu的阈值th2;Calculate the threshold th1 of Renyi entropy and the threshold th2 of Otsu respectively; 分别求出所述阈值th1对应的类间方差和所述阈值th2对应的类间方差;Respectively find the inter-class variance corresponding to the threshold th1 and the inter-class variance corresponding to the threshold th2; 根据所述阈值th1和所述阈值th2对应的所述类间方差计算得到所述类间方差的权重S1以及所述Renyi熵对应的权重S2Calculate the weight S 1 of the inter-class variance and the weight S 2 corresponding to the Renyi entropy according to the inter-class variance corresponding to the threshold th1 and the threshold th2 ; 求得分割阈值th=S1th2+S2th1;根据所述分割阈值th进行图像分割。Obtain the segmentation threshold th=S 1 th2+S 2 th1; perform image segmentation according to the segmentation threshold th. 2.根据权利要求1所述的一种基于模糊集和Otsu的图像阈值分割方法,其特征在于,求出Renyi熵的阈值th1和Otsu的阈值th2的公式包括:2. a kind of image threshold value segmentation method based on fuzzy set and Otsu according to claim 1, is characterized in that, the formula that obtains the threshold value th1 of Renyi entropy and the threshold value th2 of Otsu comprises: 其中,th1为Renyi熵的阈值;th2为Otsu的阈值;EO为原图像目标域的Renyi熵;EB为原图像背景域的Renyi熵;L为原图像的灰度级;t为灰度阈值,且t取值为[0,L–1];w0为第一类灰度出现的比例,w1为第二类灰度出现的比例,所述第一类灰度和第二类灰度根据所述灰度阈值t划分;σ0为第一类灰度对应图像的灰度均方差,σ1为第二类灰度对应图像的灰度均方差;σ为所述原图像经过所述模糊增强和所述归一化处理后的灰度平均值。Among them, th1 is the threshold of Renyi entropy; th2 is the threshold of Otsu; E O is the Renyi entropy of the target domain of the original image; E B is the Renyi entropy of the background domain of the original image; L is the gray level of the original image; t is the gray level Threshold, and the value of t is [0, L–1]; w 0 is the proportion of the first gray scale, w 1 is the proportion of the second gray scale, the first gray scale and the second gray scale The grayscale is divided according to the grayscale threshold t; σ0 is the grayscale mean square error of the image corresponding to the first type of grayscale, and σ1 is the grayscale mean square error of the image corresponding to the second type of grayscale; The average gray value after the blur enhancement and the normalization processing. 3.根据权利要求1或2所述的一种基于模糊集和Otsu的图像阈值分割方法,其特征在于,求出所述类间方差的过程包括:3. a kind of image threshold segmentation method based on fuzzy set and Otsu according to claim 1 and 2, is characterized in that, the process of obtaining variance between described classes comprises: Renyi熵的阈值th1的类间方差σ2和σ3为:The between-class variances σ2 and σ3 of the threshold th1 of Renyi entropy are: Otsu的阈值th2的类间方差σ0和σ1为:The between-class variances σ0 and σ1 of Otsu's threshold th2 are: 其中,pi为像素点数为ni的灰度级出现的概率;uT为所述原图像的灰度平均值,L1=0,L2=L–1。Among them, p i is the probability of occurrence of the gray level with the number of pixels n i ; u T is the average gray level of the original image, L1=0, L2=L–1. 4.根据权利要求3所述的一种基于模糊集和Otsu的图像阈值分割方法,其特征在于,计算得到所述类间方差的权重的过程包括:4. a kind of image threshold segmentation method based on fuzzy set and Otsu according to claim 3, is characterized in that, calculates the process that obtains the weight of described interclass variance comprising: 其中,S1为所述类间方差的权重,且S2=1–S1Wherein, S 1 is the weight of the inter-class variance, and S 2 =1−S 1 . 5.根据权利要求4所述的一种基于模糊集和Otsu的图像阈值分割方法,其特征在于,所述归一化处理包括:5. a kind of image threshold segmentation method based on fuzzy set and Otsu according to claim 4, is characterized in that, described normalization process comprises: 采用min或者max算子进行边缘提取;Use min or max operator for edge extraction; 将提取的边缘数据进行截断处理;Truncating the extracted edge data; 所述截断处理为:The truncation process is: 其中,Tr(uij)为所述边缘数据;uij为所述模糊算法中的隶属函数。Wherein, T r (u ij ) is the edge data; u ij is the membership function in the fuzzy algorithm. 6.一种基于模糊集和Otsu的图像阈值分割装置,其特征在于:包括处理器和存储器,所述处理器存储有实现如下方法的指令:6. a kind of image threshold segmentation device based on fuzzy set and Otsu, it is characterized in that: comprise processor and memory, described processor is stored with the instruction that realizes following method: 使用模糊算法对原图像进行模糊增强处理;Use the fuzzy algorithm to perform fuzzy enhancement processing on the original image; 对增强处理后的新图像进行归一化处理;Normalize the enhanced new image; 分别求出Renyi熵的阈值th1和Otsu的阈值th2;Calculate the threshold th1 of Renyi entropy and the threshold th2 of Otsu respectively; 分别求出所述阈值th1对应的类间方差和所述阈值th2对应的类间方差;Respectively find the inter-class variance corresponding to the threshold th1 and the inter-class variance corresponding to the threshold th2; 根据所述阈值th1和所述阈值th2对应的所述类间方差计算得到所述类间方差的权重S1以及所述Renyi熵对应的权重S2Calculate the weight S 1 of the inter-class variance and the weight S 2 corresponding to the Renyi entropy according to the inter-class variance corresponding to the threshold th1 and the threshold th2 ; 求得分割阈值th=S1th2+S2th1;根据所述分割阈值th进行图像分割。Obtain the segmentation threshold th=S 1 th2+S 2 th1; perform image segmentation according to the segmentation threshold th. 7.根据权利要求6所述的一种基于模糊集和Otsu的图像阈值分割装置,其特征在于,求出Renyi熵的阈值th1和Otsu的阈值th2的公式包括:7. A kind of image threshold segmentation device based on fuzzy set and Otsu according to claim 6, is characterized in that, the formula for obtaining the threshold th1 of Renyi entropy and the threshold th2 of Otsu comprises: 其中,th1为Renyi熵的阈值;th2为Otsu的阈值;EO为原图像目标域的Renyi熵;EB为原图像背景域的Renyi熵;L为原图像的灰度级;t为灰度阈值,且t取值为[0,L–1];w0为第一类灰度出现的比例,w1为第二类灰度出现的比例,所述第一类灰度和第二类灰度根据所述灰度阈值t划分;σ0为第一类灰度对应图像的灰度均方差,σ1为第二类灰度对应图像的灰度均方差;σ为所述原图像经过所述模糊增强和所述归一化处理后的灰度平均值。Among them, th1 is the threshold of Renyi entropy; th2 is the threshold of Otsu; E O is the Renyi entropy of the target domain of the original image; E B is the Renyi entropy of the background domain of the original image; L is the gray level of the original image; t is the gray level Threshold, and the value of t is [0, L–1]; w 0 is the proportion of the first gray scale, w 1 is the proportion of the second gray scale, the first gray scale and the second gray scale The grayscale is divided according to the grayscale threshold t; σ0 is the grayscale mean square error of the image corresponding to the first type of grayscale, and σ1 is the grayscale mean square error of the image corresponding to the second type of grayscale; The average gray value after the blur enhancement and the normalization processing. 8.根据权利要求6或7所述的一种基于模糊集和Otsu的图像阈值分割装置,其特征在于,求出所述类间方差的过程包括:8. a kind of image threshold segmentation device based on fuzzy set and Otsu according to claim 6 or 7, is characterized in that, the process of obtaining variance between described classes comprises: Renyi熵的阈值th1的类间方差σ2和σ3为:The between-class variances σ2 and σ3 of the threshold th1 of Renyi entropy are: Otsu的阈值th2的类间方差σ0和σ1为:The between-class variances σ0 and σ1 of Otsu's threshold th2 are: 其中,pi为像素点数为ni的灰度级出现的概率;uT为所述原图像的灰度平均值,L1=0,L2=L–1。Among them, p i is the probability of occurrence of the gray level with the number of pixels n i ; u T is the average gray level of the original image, L1=0, L2=L–1. 9.根据权利要求8所述的一种基于模糊集和Otsu的图像阈值分割装置,其特征在于,计算得到所述类间方差的权重的过程包括:9. a kind of image threshold segmentation device based on fuzzy set and Otsu according to claim 8, is characterized in that, calculates the process that obtains the weight of described interclass variance comprising: 其中,S1为所述类间方差的权重,且S2=1–S1Wherein, S 1 is the weight of the inter-class variance, and S 2 =1−S 1 . 10.根据权利要求9所述的一种基于模糊集和Otsu的图像阈值分割装置,其特征在于,所述归一化处理包括:10. a kind of image threshold segmentation device based on fuzzy set and Otsu according to claim 9, is characterized in that, described normalization process comprises: 采用min或者max算子进行边缘提取;Use min or max operator for edge extraction; 将提取的边缘数据进行截断处理;Truncating the extracted edge data; 所述截断处理为:The truncation process is: 其中,Tr(uij)为所述边缘数据;uij为所述模糊算法中的隶属函数。Wherein, T r (u ij ) is the edge data; u ij is the membership function in the fuzzy algorithm.
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